EXAMPLE 2 Finding the mean and standard deviation of the sampling distribution of

According to the American Time Use Survey, the mean amount of sleep that 20- to 24-year-old women get per night is 9.3 hours (Source: Bureau of Labor Statistics1). Assume that the population standard deviation is hour. Find the mean and standard deviation for the sampling distribution of for the following sample sizes: (a) 4, (b) 100, (c) 400.

Solution

We have . Note that this value for does not depend on the sample size, so the value is true for any sample size. We also have .

  1. . Then, The standard error of the mean for is .
  2. . Then, standard error
  3. . Then, standard error

NOW YOU CAN DO

Exercises 9–16.